Given, quadratic equation is ax2+ax+5=0 For a quadratic equation Ax2+Bx+C=0 to have no real roots, ∆=B2−4AC<0 So, ‌‌∆=a2−4(a)(5)<0 ‌⇒‌‌a2−20a<0 ‌⇒‌‌a(a−20)<0 So, $lquad 0 Thus, a must be an integer. So, the integral values of a in this range are 1,2,3,ldots,19. The number of such value is $ 19-1+1=19 $